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Beyond GDP?Welfare across Countries and Time
Chad Jones and Pete Klenow
Stanford University and NBER
November 10, 2010
Comparing welfare across countries and over time
How successful is an economy at delivering the highest possiblewelfare for its citizens?
• Fundamental question at the heart of economic growth anddevelopment
• Per capita GDP is our standard (shortcut) answer
• Can we do better?
GDP per capita 6= Welfare
Utility depends on:
• Consumption
• Life Expectancy
• Leisure
• Inequality
• ...
But GDP per capita “only” measures income...
Motivating Example 1: France vs. the U.S.
U.S. has higher private consumption
But compared to the U.S., France has:
• More leisure
• Less inequality
• More public consumption (percentage)
• Longer life expectancy
Which country delivers higher welfare, the U.S. or France?
Motivating Example 2: Growth in China
Income has been growing rapidly in China
Amidst the growth:
• Leisure has fallen
• Inequality has risen
• The saving rate has risen (bad, controlling for income!)
• Life expectancy has lengthened
Has welfare risen faster or slower than income in China?
What We Do
Assume:
• Perspective of one set of preferences (those of “Rawls”)
• Popular functional form over consumption, leisure, lifespan
• Parameters to match U.S. consumption, leisure, value of life
Evaluate outcomes using a particular set of preferences:
• Expected utility “behind the Rawlsian veil” in each country-year
• Flow measure of welfare, not PDV
• Fraction of U.S. consumption which makes “Rawls” indifferent
Two approaches:
• Macro calculation: Macro data for 134 countries.• Micro calculation: Household surveys for 5 countries.
Important Shortcomings of our Approach
Factors we do not capture
• Morbidity (other than through health spending)
• Quality of the natural environment
• Political freedoms
• Crime
• ....
But neither does income!
Summary of Results
• Income and welfare are highly correlated in both levels andgrowth rates.
• Nevertheless, differences between income and welfare areeconomically important:
– Median deviation in levels is over 40 percent.
– Median deviation in growth rates is about 1 percentage point.
Related Literature
Nordhaus and Tobin’s “Measure of Economic Welfare”
• Consumption and Leisure in the U.S. over time• No Inequality or Life Expectancy, no country comparisons
U.N. Human Development Index
• Adds [0,1] Income, Life Expectancy, Literacy• But no Consumption, Leisure, Inequality, or changes over time
Becker, Philipson, and Soares (2005)
• Combines per capita GDP and life expectancy⇒“full income”• Mainly focused on evolution of cross-section dispersion
Fleurbaey and Gaulier (2009)
• Full-income measure of life expectancy, leisure, and inequality• OECD only, levels only, not consumption-based
Theory Underlyingthe Macro Calculations
Let Rawls “live” for a year as a random person in some country,facing their mortality rates and consumption/leisure distribution.
Overview of Welfare
Expected utility behind the Rawlsian veil of ignorance:
V(e, c, `, σ) = e(
u + log c + v(`)− 12σ2)
Preferences
• Let C denote an individual’s consumption.— Independent of age.
• Let ` denote leisure or time spent in home production.
• Flow utility in benchmark case
u(C, `) = u + log C + v(`)
• u influences the value of life given C, `.
Life Expectancy
• Rawls draws ageUniform[0,100]
• Faces thecross-sectionalmortality rates for2000 in a country
• p = probabilitylives instead of dies
p = e/100 0 1000
1
Age, a
Probability of Survival to Age a
LifeExpectancy, e
• Expected utility — normalizing death to be 0:
p · u(C, `) + (1− p) · 0 = e · u(C, `)/100.
Inequality in Consumption
Suppose consumption C is log-normally distributed.
• Arithmetic mean c (consumption per capita).
• Standard deviation σ.
Conditional on being alive, expected utility from consumption is:
E[log C] = log c− 12· σ2
Rawlsian Utility for a Country
Assumptions for Macro Calculation:
• Assume survival rates S(a) are independent of consumption.
• Assume log-normal consumption independent of age.
• Assume no inequality in leisure.
Expected utility behind the Rawlsian veil of ignorance:
V(e, c, `, σ) = e(
u + log c + v(`)− 12σ2)
Comparing Welfare Across Countries
What makes Rawls indifferent between the U.S. and country i?
One answer:Scaling U.S. consumption by some proportion λi.
V(eus, λicus, `us, σus) = V(ei, ci, `i, σi)
Decomposing Welfare Differences Across Countries
logλi = ei−euseus
(u + log ci + v(`i)− 12σ
2i ) Life Expectancy
+ log ci − log cus Consumption
+ v(`i)− v(`us) Leisure
−12(σ2
i − σ2us) Inequality
As a ratio to per capita GDP
log λiyi
= ei−euseus
(u + log ci + v(`i)− 12σ
2i ) Life Expectancy
+ log ci/yi − log cus/yus Consumption Share
+ v(`i)− v(`us) Leisure
−12(σ2
i − σ2us) Inequality
Equivalent vs. Compensating Variation
What makes Rawls indifferent between the U.S. and country i?
Alternative answer:Scaling foreign consumption by some proportion λi.
V(eus, cus, `us, σus) = V(ei, ci/λi, `i, σi)
Decomposing Welfare based on Compensating Variations
logλi = ei−eusei
(u + log cus + v(`us)− 12σ
2us) Life Expectancy
+ log ci − log cus Consumption
+ v(`i)− v(`us) Leisure
−12(σ2
i − σ2us) Inequality
Baseline: report the geometric average of thecompensating and equivalent variations.
Decomposing Welfare Differences Across Time
logλt,t+1 =et+1−et
et+1(u + log ct + v(`t)− 1
2σ2t ) Life Expectancy
+ log ct+1 − log ct Consumption
+ v(`t+1)− v(`t) Leisure
−12(σ2
t+1 − σ2t ) Inequality
Baseline: report the geometric average of thecompensating and equivalent variations.
Macro Data Sources
Penn World Table 6.3 (National Accounts + World Bank ICP):
• Income• Private consumption, government consumption• Employment / adult population
World Bank:
• Life Expectancy
OECD and ILO:
• Annual hours worked per worker (OECD)• Average annual weekly hours worked in manufacturing (ILO)
United Nations World Income Inequality Database:
• Gini Coefficients
Leisure / Home Production
` = 1− annual hours worked per worker16× 365
· employmentadult population
.
• Annual hours worked per worker– SourceOECD has data for OECD countries (30 countries)– ILO has weekly hours worked in manufacturing for an additional
56 countries. Use regression to impute annual hours overall.– For remaining countries, just use average value based on income
above/below 0.5 × U.S. income
• Employment per adult population– From Penn World Tables and World Bank– Implicitly assumes kids and adults have same leisure/hp.
• Micro calculation uses hours per year from household surveys,varying across people.
Intensive and Extensive Margins of Work
0.4 0.5 0.6 0.7 0.8 0.91200
1400
1600
1800
2000
2200
2400
2600
Austria
Belgium
Canada
Czech Republic
Denmark France
Germany
Greece Hungary
Iceland
Ireland
Italy Japan
South Korea
Luxembourg
Mexico
Netherlands
Norway
Poland
Spain
Sweden Switzerland
Turkey
United Kingdom
United States
Bangladesh Bolivia Brazil
Bulgaria
Chile
China
Colombia Croatia
Egypt
Estonia
Gambia
India
Indonesia
Israel
Jamaica
Jordan
Kazakhstan
Kenya
Kyrgyzstan
Malta
Moldova
Nepal
Nicaragua Paraguay
Peru
Puerto Rico
Singapore
South Africa
Sri Lanka
Thailand
Ukraine
Vietnam
Employment−population ratio
Annual hours per worker
Gini Coefficients and σ2
• When consumption is log normal, there’s a one-to-one mappingbetween the gini coefficient and the standard deviation:
G = 2Φ
(σ√2
)− 1
• G is the value of the Gini coefficient.
• Φ(·) is the cdf of the standard normal distribution.
• Invert to get σ
Within-Country Inequality
1/64 1/32 1/16 1/8 1/4 1/2 1 0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Albania
Bahamas
Bangladesh Belarus
Benin
Bolivia
Botswana
Brazil
Bulgaria
Burundi
Cambodia
Cameroon
Central African Republic
Chile China Colombia
Costa Rica Cote d‘Ivoire
Djibouti
Estonia
Ethiopia Georgia Ghana
Greece
Guinea−Bissau Haiti
Hong Kong
Iceland
India Israel
Jordan
Kenya
Latvia
Lesotho
Luxembourg
Malaysia Mauritania
Mauritius
Mexico
Moldova
Namibia
Niger Nigeria
Norway
Pakistan
Panama Puerto Rico
Singapore
Slovak Republic
Somalia
South Africa
Spain
Sweden
Tanzania Thailand Uganda
United Kingdom
United States Vietnam Yemen
Zambia
Zimbabwe
GDP per person
Standard deviation of log consumption
Hungary Japan
Calibrating the Utility from Leisure
• Assume v(`) = − θε1+ε(1− `)
1+εε
• Frisch elasticity of labor supply is ε– Hall (2009a,b) surveys/reports a Frisch elasticity of 0.7 for
intensive margin and 1.9 for both margins together.– We choose ε = 1 for our baseline — results not sensitive
• Using the standard F.O.C.:
u`/uc = w =⇒ θ = w(1− τ)(1− `)−1/ε/c
• For the U.S.:
c ≈ w(1− `), τ ≈ .387, ` ≈ .797 =⇒ θ ≈ 14.9
Calibrating the Intercept in Utility
Estimates of the value of remaining life for a U.S. 40-year old:
• Range from less than $2 million to more than $6 million.• See Murphy and Topel (2006), Ashenfelter and Greenstone
(2004), Viscusi and Aldy (2003), etc.
We calibrate to $4 million in our baseline case
• This requires u ≈ 5.54 if we normalize Cus,2000 = 1• Note: u raises the value of longevity relative to c, `.
Example: Indifference Between Life and Death
• If willing to slash c to fraction f to stay alive, then:
u + log(f · c) + v(`) = 0
• The solution for u is then:
u = − log(f · c)− v(`)
u ≈ 5.54 =⇒ f ≈ 0.0053
When consumption is 0.53% of the U.S. value, flow utility turnsnegative (at `us).
Key Point 1:
(a) GDP per person highly correlated with welfare across thebroad range of countries: 0.95.
(b) Nevertheless, differences are often important: typicaldeviation is 46%.
Welfare and Income Are Correlated 0.95 in 2000
1/64 1/32 1/16 1/8 1/4 1/2 1 1/1024
1/256
1/64
1/16
1/4
1
Albania
Algeria
Bahamas
Benin
Bolivia
Bosnia
Botswana
Brazil
Burundi
Cameroon
Central African Republic
Chile
China
Cote d‘Ivoire
Djibouti
Ethiopia
France
Gambia
Germany
Greece
Guinea Guyana
Hong Kong
India
Ireland
Jordan
Kenya
South Korea
Lesotho
Luxembourg
Madagascar
Malaysia
Mali
Malta
Mauritius
Moldova
Mongolia
Namibia
Niger Nigeria
Poland
Portugal
Russia
Rwanda
Sierra Leone
Singapore
Somalia
South Africa Tajikistan
Tanzania
Tunisia
U.S.
Uzbekistan
Venezuela
Vietnam
Yemen
Zambia
Zimbabwe
GDP per person (US=1)
Welfare, λ
But Welfare typically differs from Income by about 46%
1/64 1/32 1/16 1/8 1/4 1/2 1 0
0.5
1
1.5
Albania
Armenia
Austria
Bahamas
Bangladesh
Belarus
Benin Bolivia
Bosnia
Botswana
Brazil
Bulgaria
Cambodia
Canada
Chile
China
Cote dIvoire
Croatia
Cyprus
Djibouti
Ecuador
Egypt
Ethiopia
France
Gambia
Georgia
Germany
Ghana
Greece
Guyana Haiti
Hong Kong
Hungary
Iceland
India Indonesia
Iran
Ireland
Japan
Jordan
Kenya
South Korea
Kyrgyzstan Luxembourg
Malaysia
Mali
Malta
Mauritius
Mexico
Moldova
Mongolia
Nepal
Nicaragua
Niger
Norway
Peru
Philippines
Portugal
Puerto Rico Romania
Russia
Rwanda
Senegal
Singapore
Slovenia
Somalia South Africa
Spain
Sweden
Tajikistan
Tanzania
Thailand Turkmenistan
U.K.
United States
Uzbekistan
Venezuela
Vietnam
Yemen
Zambia Zimbabwe
GDP per person (US=1)
The ratio of Welfare to Income
Key Point 2: Western Europe is much closer to the U.S. when wetake into account Europe’s longer life expectancy, additionalleisure, and lower inequality.
U.S. vs. Western Europe in 2000
—— Decomposition ——Welfare Log Lifeλ Income Ratio Exp. C/Y Leis. Ineq.
U.S. 100 100 .000 .000 .000 .000 .000
France 97.4 70.1 .329 .119 -.055 .140 .125
• Western Europe’s high taxes and generous social safety net mayreduce work effort and GDP.
• But these programs have benefits that are not measured by GDP...
U.S. vs. W. Europe in 2000
—— Decomposition ——Welfare Log Lifeλ Income Ratio Exp. C/Y Leis. Ineq.
U.S. 100.0 100.0 .000 .000 .000 .000 .00077.0 .762 .797 .675
Germany 98.0 74.0 .281 .057 -.053 .151 .12677.9 .722 .856 .452
France 97.4 70.1 .329 .119 -.055 .140 .12578.9 .721 .850 .454
Italy 89.7 69.5 .255 .155 -.113 .130 .08379.5 .681 .846 .538
U.K. 89.0 69.8 .243 .045 .036 .076 .08677.7 .789 .824 .532
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Key Point 3: Many developing countries are much poorer thanincomes suggest because of a combination of shorter lives andextreme inequality.
Welfare and Income, U.S. vs. Developed Asia in 2000
—— Decomposition ——Welfare Log Lifeλ Income Ratio Exp. C/Y Leis. Ineq.
U.S. 100.0 100.0 .000 .000 .000 .000 .00077.0 .762 .797 .675
Japan 91.5 72.4 .235 .247 -.146 .025 .10881.1 .658 .806 .489
Hong Kong 90.0 82.1 .093 .236 -.064 -.008 -.07180.9 .714 .794 .772
Singapore 43.6 82.9 -.643 .060 -.581 -.106 -.01678.1 .426 .765 .698
South Korea 29.7 47.1 -.463 -.068 -.273 -.184 .06375.9 .580 .743 .574
C/Y: 71% in Hong Kong vs. 43% in Singapore
Welfare and Income, U.S. vs. Emerging Asia in 2000
—— Decomposition ——Welfare Log Lifeλ Income Ratio Exp. C/Y Leis. Ineq.
U.S. 100.0 100.0 .000 .000 .000 .000 .00077.0 .762 .797 .675
Thailand 7.1 18.4 -.959 -.483 -.111 -.245 -.12068.3 .682 .728 .834
Indonesia 6.6 10.8 -.489 -.527 .057 -.050 .03167.5 .806 .781 .627
China 5.3 11.3 -.755 -.283 -.088 -.239 -.14571.4 .698 .729 .863
India 3.5 6.6 -.636 -.818 .148 -.009 .04362.5 .883 .794 .607
Welfare and Income, Other Emerging Markets in 2000
—— Decomposition ——Welfare Log Lifeλ Income Ratio Exp. C/Y Leis. Ineq.
U.S. 100.0 100.0 .000 .000 .000 .000 .00077.0 .762 .797 .675
Mexico 17.4 25.9 -.397 -.173 -.018 .041 -.24774.0 .748 .811 .974
Brazil 12.2 21.8 -.584 -.380 .123 -.060 -.26670.4 .861 .778 .994
Russia 8.6 20.9 -.886 -.695 -.126 .005 -.06965.3 .672 .799 .771
Welfare and Income, Sub-Saharan Africa in 2000
—— Decomposition ——Welfare Log Lifeλ Income Ratio Exp. C/Y Leis. Ineq.
U.S. 100.0 100.0 0.000 0.000 0.000 0.000 0.00077.0 .762 .797 .675
South Africa 4.4 21.6 -1.594 -1.376 0.122 0.083 -0.42356.1 .861 .826 1.140
Botswana 1.8 17.9 -2.292 -0.577 -0.171 0.028 -0.16748.9 .642 .807 .889
Malawi 0.4 2.9 -2.113 -1.952 0.254 -0.186 -0.22946.0 .982 .743 .956
South Africa: Life expectancy = 56 years⇒ factor of 4!
Key Point 4: Growth rates, 1980–2000
– Welfare: 2.5%– Income: 1.8%
Life expectancy adds more than 1.0%, except in Africa
Welfare, Income Growth 1980–2000 Correlated 0.82
−4% −2% 0% 2% 4% 6% 8% −8%
−6%
−4%
−2%
0%
2%
4%
6%
8%
Bahamas
Botswana Brazil
Cameroon
China
Colombia
Cote d‘Ivoire
Egypt
El Salvador Guatemala
Hong Kong
India
Indonesia
Ireland
Japan
Kenya
South Korea
Lesotho
Luxembourg
Madagascar
Malaysia
Mauritius
Netherlands
Nigeria
Panama
Peru
Philippines
Singapore
South Africa
Spain
Thailand Turkey
United States
Venezuela
Zambia
Per capita GDP growth
Welfare growth
Welfare vs. Income Growth, 1980–2000
−4% −2% 0% 2% 4% 6% 8% −4%
−3%
−2%
−1%
0%
1%
2%
3%
Botswana
Brazil
Bulgaria
Cameroon China
Colombia
Cote d‘Ivoire
Denmark
Egypt
El Salvador France
Guatemala
Hong Kong
India
Indonesia
Ireland
Italy
Jamaica
Japan
Kenya
South Korea
Lesotho
Luxembourg
Madagascar
Malaysia
Mauritius Mexico
Nepal
Netherlands
Nigeria
Norway
Panama
Peru
Philippines
Singapore
South Africa
Spain Thailand
Tunisia
Turkey
U.S.
Venezuela
Zambia
Per capita GDP growth
Difference between Welfare and Income growth
Key Point 5: The mean absolute deviation between welfaregrowth and income growth is 0.99 percentage points.
Welfare vs. Income Growth, Regional Averages
——— Decomposition ———Welfare Life
Country λ Income Diff Exp. C/Y Leis. Ineq.
CoastAsia 5.58 4.62 0.96 1.18 0.06 0.09 -0.37
W. Europe 3.27 2.00 1.27 1.29 -0.16 0.10 0.03
U.S. 2.59 2.04 0.55 1.09 -0.11 -0.18 -0.25
L.A. 1.57 0.41 1.15 1.78 0.05 -0.41 -0.26
SSAfrica -1.30 -0.54 -0.77 -0.15 -0.48 0.13 -0.27
Welfare vs. Income Growth, Growth Stars
——— Decomposition ———Welfare Life
Country λ Income Diff Exp. C/Y Leis. Ineq.
S Korea 7.95 5.61 2.34 2.41 -0.74 0.51 0.1665.8, 75.9 .671, .580 .718, .743 .580, .522
China 7.13 6.81 0.32 0.83 -0.07 0.08 -0.5265.5, 71.4 .708, .698 .727, .731 .443, .637
H.K. 5.54 3.61 1.94 1.70 0.42 0.37 -0.5674.7, 80.9 .656, .714 .771, .794 .681, .829
Sing. 4.94 4.74 0.20 1.67 -0.91 -0.20 -0.3571.5, 78.1 .511, .426 .777, .766 .622, .726
India 4.03 2.89 1.14 1.25 0.12 0.10 -0.3255.7, 62.5 .862, .883 .788, .794 .565, .669
Welfare vs. Income Growth, U.S. and OECD
——— Decomposition ———Welfare Life
Country λ Income Diff Exp. C/Y Leis. Ineq.
Japan 4.45 2.07 2.38 1.39 0.31 0.55 0.1376.1, 81.1 .618, .658 .771, .806 .543, .494
Italy 3.70 1.95 1.75 1.66 -0.09 0.13 0.0673.9, 79.5 .693, .681 .835, .846 .557, .536
France 3.60 1.61 1.98 1.44 -0.09 0.34 0.2974.2, 78.9 .734, .721 .822, .850 .560, .446
U.K. 3.32 2.19 1.13 1.25 -0.03 0.08 -0.1773.7, 77.7 .794, .789 .818, .824 .448, .520
U.S. 2.59 2.04 0.55 1.09 -0.11 -0.18 -0.2573.7, 77.0 .778, .762 .809, .797 .601, .680
Welfare vs. Income Growth, U.S. and OECD
——— Decomposition ———Welfare Life
Country λ Income Diff Exp. C/Y Leis. Ineq.
Japan 4.45 2.07 2.38 1.39 0.31 0.55 0.1376.1, 81.1 .618, .658 .771, .806 .543, .494
Italy 3.70 1.95 1.75 1.66 -0.09 0.13 0.0673.9, 79.5 .693, .681 .835, .846 .557, .536
France 3.60 1.61 1.98 1.44 -0.09 0.34 0.2974.2, 78.9 .734, .721 .822, .850 .560, .446
U.K. 3.32 2.19 1.13 1.25 -0.03 0.08 -0.1773.7, 77.7 .794, .789 .818, .824 .448, .520
U.S. 2.59 2.04 0.55 1.09 -0.11 -0.18 -0.2573.7, 77.0 .778, .762 .809, .797 .601, .680
Welfare vs. Income Growth, Developing Countries
——— Decomposition ———Welfare Life
Country λ Income Diff Exp. C/Y Leis. Ineq.
Mexico 1.83 0.53 1.30 1.81 -0.01 -0.32 -0.1966.8, 74.0 .749, .748 .835, .811 .827, .871
Brazil 1.76 0.18 1.59 1.88 0.23 -0.44 -0.0862.8, 70.4 .822, .861 .796, .769 .957, .973
Botswa. 1.20 4.35 -3.16 -2.72 -0.88 0.29 0.1660.5, 48.9 .766, .642 .783, .801 .906, .871
SAfrica -0.89 0.10 -0.99 -0.32 0.14 0.15 -0.9657.2, 56.1 .837, .861 .807, .818 .762, .981
Robustness
Key Points are all qualitatively robust.
Sensitivity of magnitudes in order of importance:
• CV versus EV• u — U.S. value of life• K/Y: current level versus steady state• Coefficient of relative risk aversion• Parameterization of utility from leisure
Robustness — Summary Results
# of countries— Median absolute deviation — with negative
Robustness check Levels Growth rate flow utility
Benchmark case 0.379 0.99 0
Equivalent variation 0.269 0.93 0Compensating variation 0.442 1.03 0γ = 1.5, c = 0 0.329 0.61 52γ = 1.5, c = .088 0.386 0.86 6γ = 2.0, c = .271 0.414 0.96 6θ from FOC for France 0.413 1.05 0Frisch elasticity = 1.9 0.383 0.98 0Value of Life = $3m 0.286 0.73 14Value of Life = $5m 0.464 1.39 0
Robustness — France (y = 70.1)
Welfare Log ——— Decomposition ———Country λ Ratio L.E. C/Y Leis. Ineq.
Benchmark case 97.4 0.329 0.119 -0.055 0.140 0.125
Equivalent variation 97.3 0.329 0.118 -0.055 0.140 0.125Compensating variation 97.4 0.329 0.119 -0.055 0.140 0.125γ = 1.5, c = 0 102.8 0.383 0.097 -0.055 0.153 0.186γ = 1.5, c = .088 102.3 0.378 0.108 ... 0.163 0.160γ = 2.0, c = .271 105.5 0.410 0.108 ... 0.186 0.168θ from FOC for France 109.0 0.442 0.114 -0.055 0.258 0.125Frisch elasticity = 1.9 98.3 0.339 0.119 -0.055 0.150 0.125Value of Life = $3m 94.1 0.295 0.085 -0.055 0.140 0.125Value of Life = $5m 100.7 0.363 0.152 -0.055 0.140 0.125
Baseline Welfare Measure, 2000
1/64 1/32 1/16 1/8 1/4 1/2 1 1/1024
1/256
1/64
1/16
1/4
1
Albania
Algeria
Bahamas
Benin
Bolivia
Bosnia
Botswana
Brazil
Burundi
Cameroon
Central African Republic
Chile
China
Cote d‘Ivoire
Djibouti
Ethiopia
France
Gambia
Germany
Greece
Guinea Guyana
Hong Kong
India
Ireland
Jordan
Kenya
South Korea
Lesotho
Luxembourg
Madagascar
Malaysia
Mali
Malta
Mauritius
Moldova
Mongolia
Namibia
Niger Nigeria
Poland
Portugal
Russia
Rwanda
Sierra Leone
Singapore
Somalia
South Africa Tajikistan
Tanzania
Tunisia
U.S.
Uzbekistan
Venezuela
Vietnam
Yemen
Zambia
Zimbabwe
GDP per person (US=1)
Welfare, λ
Equivalent Variation, 2000
1/64 1/32 1/16 1/8 1/4 1/2 1 1/128
1/64
1/32
1/16
1/8
1/4
1/2
1
Albania
Algeria
Armenia
Australia Austria
Azerbaijan
Bahamas
Bangladesh
Belarus
Belgium
Benin
Bolivia
Bosnia and Herzegovina
Botswana
Brazil
Bulgaria
Burkina Faso
Burundi
Cambodia Cameroon
Canada
Central African Republic
Chile
China
Colombia
Costa Rica
Cote d‘Ivoire
Croatia
Cyprus
Czech Republic
Denmark
Djibouti
Dominican Republic
Ecuador Egypt El Salvador
Estonia
Ethiopia
Fiji
Finland
France
Gambia
Georgia
Germany
Ghana
Greece
Guatemala
Guinea
Guinea−Bissau
Guyana Haiti
Honduras
Hong Kong
Hungary
Iceland
India
Indonesia
Iran
Ireland Israel
Italy
Jamaica
Japan
Jordan Kazakhstan
Kenya
South Korea
Kyrgyzstan
Laos
Latvia
Lesotho
Lithuania
Luxembourg
Macedonia
Madagascar Malawi
Malaysia
Mali
Malta
Mauritania
Mauritius
Mexico
Moldova
Mongolia
Mozambique
Namibia Nepal
Netherlands
New Zealand
Nicaragua
Niger Nigeria
Norway
Pakistan
Panama
Papua New Guinea
Paraguay Peru Philippines
Poland
Portugal Puerto Rico
Romania
Russia
Rwanda
Senegal
Sierra Leone
Singapore
Slovak Republic
Slovenia
Somalia
South Africa
Spain
Sri Lanka
Swaziland
Sweden Switzerland
Tajikistan
Tanzania
Thailand
Trinidad &Tobago Tunisia
Turkey
Turkmenistan
Uganda
Ukraine
United Kingdom United States
Uzbekistan
Venezuela
Vietnam
Yemen
Zambia
Zimbabwe
GDP per person (US=1)
Welfare, λ
Compensating Variation, 2000
1/64 1/32 1/16 1/8 1/4 1/2 1
1/4096
1/1024
1/256
1/64
1/16
1/4
1
Albania
Algeria
Armenia
Australia Austria
Azerbaijan
Bahamas
Bangladesh
Belarus
Belgium
Benin
Bolivia
Bosnia and Herzegovina
Botswana
Brazil Bulgaria
Burkina Faso
Burundi
Cambodia Cameroon
Canada
Central African Republic
Chile
China
Colombia
Costa Rica
Cote d‘Ivoire
Croatia
Cyprus
Czech Republic
Denmark
Djibouti
Dominican Republic Ecuador Egypt El Salvador
Estonia
Ethiopia
Fiji
Finland France
Gambia
Georgia
Germany
Ghana
Greece
Guatemala
Guinea
Guinea−Bissau
Guyana
Haiti
Honduras
Hong Kong
Hungary
Iceland
India
Indonesia
Iran
Ireland Israel Italy
Jamaica
Japan
Jordan Kazakhstan
Kenya
South Korea
Kyrgyzstan
Laos
Latvia
Lesotho
Lithuania
Luxembourg
Macedonia
Madagascar
Malawi
Malaysia
Mali
Malta
Mauritania
Mauritius
Mexico
Moldova
Mongolia
Mozambique
Namibia Nepal
Netherlands New Zealand
Nicaragua
Niger
Nigeria
Norway
Pakistan
Panama
Papua New Guinea
Paraguay Peru Philippines
Poland
Portugal Puerto Rico
Romania
Russia
Rwanda
Senegal
Sierra Leone
Singapore Slovak Republic
Slovenia
Somalia
South Africa
Spain
Sri Lanka
Swaziland
Sweden Switzerland
Tajikistan
Tanzania
Thailand
Trinidad &Tobago Tunisia
Turkey
Turkmenistan
Uganda
Ukraine
United Kingdom United States
Uzbekistan
Venezuela
Vietnam
Yemen
Zambia
Zimbabwe
GDP per person (US=1)
Welfare, λ
Adjusting the Consumption Share for Transition Dynamics
0.2 0.4 0.6 0.8 10.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Algeria
Bahamas
Bangladesh
Bolivia
Botswana
Brazil
Bulgaria
Burundi Cameroon
China Colombia
Costa Rica
Djibouti
Ethiopia Gambia
Germany
Ghana
Greece
Guatemala
Guinea
Guyana
Haiti
India
Iraq
Ireland
Japan
South Korea Luxembourg
Madagascar
Malawi
Malaysia
Mauritania
Mauritius
Mongolia
Nepal
Norway
Paraguay Philippines
Portugal
Romania
Rwanda
Senegal Sierra Leone
Singapore
Somalia
South Africa
Sweden
Thailand
United States
Venezuela
Vietnam
Zimbabwe
C / Y
(C / Y)ss
Robustness: Inferring C/Y from K/Y , 2000
Rising I/Y ⇒ (C/Y)adj > C/YPer capita Benchmark Welfare w/ Benchmark Adjusted
Country Income welfare C/Y adj. C/Y C/Y
United States 100.0 100.0 100.0 0.762 0.792
Germany 74.0 98.0 86.9 0.722 0.666
France 70.1 97.4 89.9 0.721 0.693
Japan 72.4 91.5 73.7 0.658 0.554
Hong Kong 82.1 90.0 86.6 0.714 0.715
U.K. 69.8 89.0 86.1 0.789 0.795
Singapore 82.9 43.6 46.9 0.426 0.477
South Korea 47.1 29.7 30.1 0.580 0.611
China 11.3 5.3 5.9 0.698 0.810
India 6.6 3.5 3.5 0.883 0.911
Micro Calculations
Household Surveys for various country-years
• Household expenditures
• Age, Hours Worked of each household member
Have analyzed micro data for:
• U.S. (1984–2006)
• France(1984–2005)
• India (1984-2005)
• Mexico(1984-2002)
• South Africa(1993)
10 Advantages to Micro Calculations
• Make sure consumption (not income) inequality
• Allow arbitrary (non-normal) distribution of consumption
• Drop durables (lumpy)
• Individual (rather than household) consumption
• Better measure of hours worked if non-OECD
• Incorporate inequality in leisure
• Adjust for age composition of population
• Incorporate survival rates by age
• Uniform use of sampling weights
• Allow government consumption to lower inequality (if desired)
Theory for the Micro Calculation
• Basic notation:a ≡ agej ≡ people within age groupSi
a ≡ Probability of surviving to age a in country i
• Mortality notation
susa ≡
Susa∑
a Susa
∆sia ≡
Sia − Sus
a∑a Sus
a
• Demographically-adjusted averages:
ci ≡∑
a
susa
∑j
ωijaci
ja
¯i ≡∑
a
susa
∑j
ωija`
ija
Micro Welfare Decomposition
logλi =∑
a ∆siaui
a Life Exp.
+ log ci − log cus Consumption
+v(¯i)− v(¯us) Leisure
+E log ci − log ci − (E log cus − log cus) Cons. Ineq.
+Ev(`i)− v(¯i)−(Ev(`us)− v(¯us)
)Leis. Ineq.
Micro Calculations: Levels
—— Decomposition ——Welfare Log Life Cons Leisλ Income Ratio Exp. C/Y Leis. Ineq Ineq
France 103.8 68.7 .413 .132 -.088 .117 .116 .135(macro) 97.4 70.1 .329 .119 -.055 .140 .125 ...
India 4.9 8.0 -.487 -.614 .102 .002 .050 -.027(macro) 3.5 6.6 -.636 -.818 .148 .009 .043 ...
Mexico 18.7 25.7 -.319 -.146 -.013 .019 -.170 -.010(macro) 17.4 25.9 -.397 -.173 -.018 .041 -.247 ...
S Africa 8.5 22.6 -.744 -.609 .217 .084 -.427 -.008(macro) 4.4 21.6 -1.594 -1.376 .122 .083 -.423 ...
Micro Calculations: Growth Rates
—— Decomposition ——Welfare Income Life Cons. Leis.Growth Growth Diff Exp. C/Y Leis. Ineq. Ineq
France 2.46 1.64 0.82 .91 -.10 -.02 .00 .03(macro) 3.60 1.61 1.98 1.44 -.09 .34 .29 ...
India 3.69 3.68 .01 .52 -.38 .02 -.17 .01(macro) 3.11 2.89 .22 .48 .12 -.06 -.32 ...
Mexico 1.24 0.83 .41 .78 -.13 -.08 -.24 -.07(macro) 0.61 0.53 .08 1.14 -.01 -.87 -.19 ...
U.S. 2.39 1.94 .45 .70 .00 -.33 -.01 .09(macro) 2.08 2.04 .05 .76 -.11 -.36 -.25 ...
Conclusions
• Income and welfare are highly correlated in both levels andgrowth rates.
• Nevertheless, differences between income and welfare are ofteneconomically important:
– Western Europe looks much closer to U.S. living standards.
– Most other countries are further behind, primarily due to lowerlife expectancy.
– Longer lives add over one percentage point, on average, towelfare growth per year 1980–2000.